Here's my attempt at calculating Mars solar time for Deimos Image 1:

1. Sol 038 ended at 8:13 a.m. PST or 16:13 in UTC (Pacific time is UTC -8)
2. So Mars midnight at Opportunity was UTC 16:13 March 3
3. UTC 03:03:43 (see below) the next day March 4 is 10.82138 Earth hours later
4. 10.82138 Earth hours is 10.52889 Mars hours or 10:31:44 Mars time

Contrast with the given Mars time of 10:28:17, but closer to the JPL Horizons time of 10:30:14 for the start of the transit.

If I've not made a miscalculation, and if Opportunity's onboard clock was correct, then UTC times for the 4 Deimos transit images (see [1]) were:

Mar 4 03:03:43 = Image 1 showing mid-transit
Mar 4 03:03:53 = Image 2 still in transit
Mar 4 03:04:03 = Image 3 approaching third contact
Mar 4 03:04:13 = Image 4 possibly between third and fourth contact

Compare with the 3 Opportunity images mentioned in IAU circular 08298:

Mar 4 03:03:56  Mar. 4.12773 UT
Mar 4 03:04:06  Mar. 4.12785
Mar 4 03:04:35  Mar. 4.12819

My rough work, MER-0 is 0 seconds for the Rover clock:

UTC decimal       HH:MM:SS  Julian Day     secs since MER-0
-----------------------------------------------------------
2000 Jan 1 noon =           2451545.0             64.184
2004 Mar 3 noon =           2453068.0      131587264.184 =1523 days +64secs
2004 Mar 4.127581 03:03:43  2453068.627581 131641487.0   = Image 1
2004 Mar 4.127697 03:03:53  2453068.627697 131641497.0   = Image 2
2004 Mar 4.127812 03:04:03  2453068.627812 131641507.0   = Image 3
2004 Mar 4.127928 03:04:13  2453068.627928 131641517.0   = Image 4

Probably some false assumptions in the above, of course. -Wikibob | Talk 22:56, 2004 Jun 20 (UTC)

Ah, I see, the original image filenames contain a timestamp, in seconds since the J2000.0 epoch, as per [2].

I verified that January 1 2000 11:58:55.816 UTC + 131641487 seconds = March 4 2004 03:03:42.816, and the other images are at ...497, ...507, ...517 seconds. So your calculations above are exact.

The Spirit images, on the other hand are timestamped 132408331, ...341, ...351, up to ...401, which corresponds to March 13 2004 00:04:26.816 UTC for the first and then 10 second intervals thereafter. The last image therefore is 70 seconds later, or 00:05:36.816

It's possible that the onboard clock gains or loses time, and doesn't correspond to the exact time. But on the other hand, the JPL Horizons ephemeris data for Phobos and Deimos might have some slight inaccuracy as well.

-- Curps 00:35, 21 Jun 2004 (UTC)

As I mentioned on your talk page, there's something fishy about the times given in the IAU Circular, because there is a timespan of 40 seconds between the first and last times given, whereas the actual timespan can only have been 30 seconds (0,10,20,30 for the 4 images).

-- Curps 00:38, 21 Jun 2004 (UTC)

I presume Sol 38 didn't end at exactly 16:13:00.000 UTC.

According to JPL Horizons, by local apparent solar time Sol 38 ended at 2004-Mar-03 16:16:26.504 UTC at the Opportunity landing site. No doubt the solar times quoted for the mission are some form of mean solar time.

Still, I presume the reported time of 8:13 a.m. PST was rounded to the nearest minute.

As before, a Mars hour is 1.027491251 times longer than an Earth hour, but unless we have a more exact value for the PST or UTC time of the start of Sol 38 I don't think we can go any further.

-- Curps 04:07, 21 Jun 2004 (UTC)